what is a dual vector space. How can i get dual space from given vector space. What are the characteristics of this dual space. It physical meaning and application. With what condition dual space and vector space are same.
How a column vector in vector space become row vector in dual space.

Question

what is a dual vector space. How can i get dual space from given vector space. What are the characteristics of this dual space. It physical meaning and application. With what condition dual space and vector space are same.
How a column vector in vector space become row vector in dual space.

anonymous · Answer

I have studied vector spaces and linear transformation.

goformit100 · Answer

In mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors. When applied to vector spaces of functions (which typically are infinite-dimensional), dual spaces are employed for defining and studying concepts like measures, distributions, and Hilbert spaces. Consequently, the dual space is an important concept in the study of functional analysis.

There are two types of dual spaces: the algebraic dual space, and the continuous dual space. The algebraic dual space is defined for all vector spaces. When defined for a topological vector space there is a subspace of this dual space, corresponding to continuous linear functionals, which constitutes a continuous dual space.

goformit100 · Answer

ok?

anonymous · Answer

no, what is dual space???? in simple words........

goformit100 · Answer

In simple words dual space means Oh! Peter should try it first.

anonymous · Answer

... I don't even...

anonymous · Answer

If you have a vector space V over a field F, then the dual space is:$$V^* =\mbox{Hom}(V,F)$$In other words, its the set of all linear transformations from the vector space to the field itself.  A linear transformation from a vector space to the field it is over is called a lienar functional.

anonymous · Answer

please complete the answer.

anonymous · Answer

What you are asking for is a lot, and a little vague.  I can guide you to a helpful book (Linear Algebra, by Hoffman-Kunze), or I could help with a specific problem, but just the question, "What are the characteristics of a dual space"  is a complete chapter in a text book, which I'm am not going to type up here.